## The bidiagonal singular values decomposition and Hamiltonian mechanics (1991)

Venue: | SIAM J. Num. Anal |

Citations: | 25 - 6 self |

### BibTeX

@ARTICLE{Deift91thebidiagonal,

author = {Percy Deift and James Demmel and Chau Li and Carlos Tomei},

title = {The bidiagonal singular values decomposition and Hamiltonian mechanics},

journal = {SIAM J. Num. Anal},

year = {1991}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider computing the singular value decomposition of a bidiagonal matrixB. This problem arises in the singular value decomposition of a general matrix, and in the eigenproblem for a symmetric positive de nite tridiagonal matrix. We show that if the entries of B are known with high relative accuracy, the singular values and singular vectors ofB will be determined to much higher accuracy than the standard perturbation theory suggests. We also show that the algorithm in [Demmel and Kahan] computes the singular vectors as well as the singular values to this accuracy. We also give a Hamiltonian interpretation of the algorithm and use di erential equation methods to prove many of the basic facts. The Hamiltonian approach suggests a way to use ows to predict the accumulation of error in other eigenvalue algorithms as well.